Loose Hamiltonian cycles forced by large $(k-2)$-degree - approximate version

Josefran de Oliveira Bastos, Guilherme Oliveira Mota, Mathias Schacht +2

We prove that for all $k\ge 4$ and $1\le \ell <k/2$, every $k$-uniform hypergraph $\mathcal{H}$ on $n$ vertices with $δ_{k-2}(\mathcal{H})\geq\left(\frac{4(k-\ell)-1}{4(k-\ell)^2}+…